Good reductions of CM points for Exceptional Shimura Varieties
Jacob Tsimerman (University of Toronto)
Abstract: Given an Elliptic curve E with complex multiplication, it is known that E has (potentially) good reduction everywhere. Concretely, this means that the j-invariant of E is an algebraic integer. The generalization of this result to Abelian-Varieties follows from the Neron-Ogg-Shafarevich criterion for good reduction.
We generalize this result to Exceptional Shimura varieties S. Concretely, we show that there exists some integral model S_0 of S such that all special points of S extend to integral points of S_0. To prove this we establish a Neron-Ogg-Shafarevich criterion in this setting. Our methods are general and apply, in particular, to arbitrary variations of hodge structures with an immersive Kodaira-Spencer map.
We will explain the proof (which is largely in the realm of birational p-adic geometry) and the open questions that remain. This is joint work with Ben Bakker.
number theory
Audience: researchers in the topic
| Organizers: | Sol Friedberg*, Benjamin Howard, Dubi Kelmer, Spencer Leslie, Keerthi Madapusi Pera, Bjorn Poonen*, Andrew Sutherland*, Wei Zhang* |
| *contact for this listing |